Anisotropic Polarized Emission of a Doped Silicon Lamellar Grating

[+] Author and Article Information
F. Marquier, M. Laroche, R. Carminati, J.-J. Greffet

 Laboratoire d’Énergétique Moléculaire et Macroscopique; Combustion, École Centrale Paris, Centre National de la Recherche Scientifique, Grande Voie des Vignes, 92295 Châtenay-Malabry Cedex, France

J. Heat Transfer 129(1), 11-16 (Jun 21, 2006) (6 pages) doi:10.1115/1.2360594 History: Received January 24, 2006; Revised June 21, 2006

Thermal emission of a doped silicon grating has been studied in the plane perpendicular to the grooves. We show how the excitation of surface plasmons produce a resonant emission weakly depending on the polarization and azimuthal angle. We analyze in detail the polarization and angular dependence of the emission out of the plane perpendicular to the grooves. Two kinds of thermal sources, directional and quasi-isotropic, are studied. They have been designed in a previous paper. We also compute the total hemispherical emissivity of these gratings. In addition we show that in applications such as radiative cooling, these sources are less efficient than other structures.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 7

Polar representation of the emissivity at λ=5.9μm for the quasi-isotropic source in both p-polarization (a) and s-polarization (b)

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Figure 8

Polar representation of the average emissivity in both p- and s-polarization at λ=5.9μm for the quasi-isotropic source

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Figure 4

Polar representation of the emissivity at λ=8.0μm for the directional source in both p-polarization (a) and s-polarization (b)

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Figure 5

Dispersion relation of surface plasmon-polaritons in a (kx,ky) plane for a fixed frequency on a grating. The radius of the dashed circle is the wave vector modulus in free space. Inside this circle (in gray), the emitted waves have a real z-component of k, so that they are propagating waves. Outside the dashed circle, the waves are evanescent waves. The solid circle at the center has a radius equal to the modulus of the wave vector of the surface plasmon-polariton kSP. With a grating of period Λ, this solid circle is reproduced with a period 2π∕Λ: It represents the surface waves diffraction at the orders ±1. One can see that a part of the solid line is lying now in the light cone, so that the corresponding surface plasmon-polaritons are coupled to propagating waves.

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Figure 6

Wave vector diagram of a lamellar grating periodic along the x-axis. The material can support surface waves.

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Figure 1

Emission of a grating in the direction (θ,ϕ). The electric field E makes an angle Ψ with the plane (z,k). Ψ=0deg corresponds to the p-polarization and Ψ=90deg to the s-polarization.

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Figure 2

Emissivity pattern in p-polarization for p-doped silicon gratings with N=2.5×1020cm−3 (the grooves of the grating are perpendicular to the incident plane: ϕ=0deg). (a) Directional source with parameters Λ=6.3μm, F=0.4 and h=0.6μm. (b) Quasi-isotropic source with Λ=2.5μm, F=0.8, and h=0.6μm.

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Figure 3

Solid line: Schematic dispersion relation of a surface plasmon polariton. Dashed line: Light cone. The solid curve lies out of the light cone, so that the wave is evanescent. k‖ is the projection of the wave vector in the plane (x,y), and ω=2πc∕λ is the pulsation.



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